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                路径统计path                </h1>
                <p>时间限制：5s&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  空间限制：162MB</p>			</div>
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                                <h3>题目描述</h3><p>
	
一个矩阵由r行c列共r*c个小正方形组成。行从下到上编号为1到r，列从左到右编号为1到c。所有坐标都是(row,colmn)的形式。
给出n个特殊点的坐标，保证特殊点在矩阵内，依次编号为1到n，从(1,1)到(r,c)的包含严格k个特殊点的路径称为k型路径。
同时路径必须遵循以下规则：
1.	每次你只能向上或向右。即你只能从(x,y)走到(x+1,y)或(x,y+1)
2.	特殊点在路径中出现的顺序必须与给出的顺序相同，即如果特殊点a出现在特殊点b之前，那么a必须小于b。
请输出0型路径，1型路径…,n型路径的条数mod 1000007
</p><hr/><h3>输入格式</h3><p>第一行两个数R,C。
第二行描述1-n号特殊点的行号。请读到行尾。
第二行描述1-n号特殊点的列号。

</p><hr/><h3>输出格式</h3><p>N+1个用空格隔开的整数，分别表示1型路径…,n型路径的条数mod 1000007

</p><hr/><h3>样例输入</h3><pre>3
3
2 3
2 2

</pre><hr/><h3>样例输出</h3><pre>1 3 2

【样例解释】
0型路径
(1, 1) -> (1, 2) -> (1, 3) -> (2, 3) -> (3, 3)
1型路径
(1, 1) -> (2, 1) -> (2, 2) -> (2, 3) -> (3, 3)
(1, 1) -> (1, 2) -> (2, 2) -> (2, 3) -> (3, 3)
(1, 1) -> (2, 1) -> (3, 1) -> (3, 2) -> (3, 3)
2型路径
(1, 1) -> (2, 1) -> (2, 2) -> (3, 2) -> (3, 3)
(1, 1) -> (1, 2) -> (2, 2) -> (3, 2) -> (3, 3)

【数据规模】
对于100%数据
1<=R,C<=50
0<=N<=50
</pre><hr/><h3>提示</h3><p>没有写明提示</p><hr/><h3>题目来源</h3><p>没有写明来源</p>
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